The reason I asked the above was to form some opinion on how you would do on a road bike, as they are not the easiest setup to get on with if you are overweight and have no cycling experience. You are neither of those and also have plenty of time before the event.
Ultimately, the road bike is going to be the fastest in the right hands, but not the most comfortable. I would go for the lightest bike you can for the money.
The one above is about 23lb which you would have to spend quite a bit on a MTB hybrid to get that light; having some extra money for kit is wise.
I would suggest getting down to your local "decent" bike shop, so they can measure you up for a bike (you don't have to buy it there); a properly measured bike makes for a much more enjoyable ride, especially over longer distances, where a wrong fitting bike really starts to show with numbness in feet / hands etc. etc.